Southern AE greatly modified by a 1st-generation Scottish-American mother, and growing up abroad.

"Sorry for insisting" means you realize now that you shouldn't have insisted, and you regret it. It is an apologetic statement-- if you had it to do over again, you wouldn't insist.

It can also mean "sorry to insist," which means you wish you didn't have to insist, but you do. It's usually followed by the word "but."

The reason "sorry for insisting" is usually a rueful and regretful (and not just polite) expression, is that it refers to an act of insisting in the past. When you are sorry for something you did, you generally mean you feel you really shouldn't have done it.

When you're sorry for something you're doing, regret doesn't make much sense-- it's either disingenuous, or you're being gracious, using the language of apology in a contrary-to-fact manner, as is often done in courteous expressions.

The reason "sorry for insisting" is sometimes mere politeness is that it can be an elliptic way of saying "sorry that I am having to insist, but..." instead of "sorry that I did that insisting."

The difference between polite "regret" and the genuine article is mostly conveyed by tone. .
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